2003年 9月 12日
第 4 7 7 回 U R S I ―F 分 科 会 資 料

Global Distributioll of Spatial Correlation Ccemcient of Rainfall Ratelnferred from脱 圧
easurement of Spaceborne Radar

Y崎 1 0HSAKI
Colnlnullications Resear(士L LabOratOry
4‑2‑l FWukuikita―
madhi,Koganei― shi,Tokyo 184‑8975,Japanl lntroduction
rave com■11lnication links,andPrecipitation is a settous source of attenuation for llicro、
the performance of IIlicrowave coEIIllllniCation system is stronglyユIliuenced by the quan―tity and charactettstic of precipitation, Taking the spatial inhomogeneity of rainfall ratoi n t o c O n s i d e r a t i o n , M o rli tpar oapnOds eHdi gau tmHieぃ)for predictitmheotdh(OMd―rain attenuation. In ths IIlethod the spatial structure of Fain iS statistica■y represellted
e spatial correl筑
ion coemcient a of the rainfa1l rate.
,r tl■

Since the spatial structure of raln isresional
arectedけdiSerences in climate
and rain type t21,the Vttuc of 9 has dependence on regional direrences,MoritあandHigllti deterIIlined
by using
α a rain gauge network in Tokyo,Japan13卜This type of

7aluatiollis qllite laborious and has been dOne fOr few locahties. FllrthermOre,the spatiale■
correlation coerncient.leasured in Japan does not alwOys hold thttughout the world dueto the dependence on resional direrences. Thus, when the ttI―
H methOd is used for「predicting rain attenuation, the、 alue of tt deterIIlined in the relevant area should beused.The Tropical Rainfall Measuttng Mission(TRMM)is a Spaceborne radar projectof ttt Uttted States alld Japan降1.The ttst spaceborne rain radar is aboard the TRMM
satelhte. The TRttI単 質can provide quantitative measurements of rainfall over all land
and Ocean areas of the tropics. Global dist五 butioII of αhas been inferred ttom TRMIA/1
meastlrement.

2

Gilobal distribution of αrate兄 (mm/h)expreSSes the correぃ
The spatial correlation function(冴)ofβ the rainfa■
βlatibn cocttciel■
t of兄伯separated tt a distttceど)(km)・TWO types of formula for(冴Ve
beenproposed(■andれlla■),WhiCh are given by:aIIdメ〆残: ρろ,(冴) = e x p (a一■■五 :ρ(冴)=exp(一 αl″),(2)where α l(km 1)and α?(km ;)are parameters called the spatial correlation coettRcielltof兄. M a n a b e e t a l , s h o w e (d どWas appropttate for Europe) tg hi at t n βt t (E1q)。
and Morita and Higuti showed that ρ (冴)giVen tt Eq.(2)was appropriate for Japan 131.
These two types of β(ど)fOrmulas are used to estimate global distribution of a.
The standttd TRMM data products aFe Catesorized illto three lewls(1,2,andalues,andhandle engineering valucs,plvsical w‐3).Level l,2,nnd 3 products mainけ
statistical values, respectively. A■product levels are created by the National SpaceDevelopmel■t」生gency of Jttpan and the lWational Aeronautics and SPace AdministratioII.
酌質2A25 data used in this study was
M12A25 is leve1 2 product. The TRM王The TR酌 王正
ay and June 1998,and June and July 1999.TRttI酌 【Can IIleasure the rttll
IIleaslled in帥is αestimated at loIIsitude froln O to 360
at latitude±
37 degrees.Global distribution ofer grid sizeと36 degrees with grid size of 2,O by 2.O degrees,la■S「degrees,and at latitudeこis better for estilnatiIIg 810bal distribution withof αine spatial resolution. However,asgrid size becomes smaller,the amount of data in eacSh grid becomes smaller. A sumcientline αaIIount of data should be used to deter■,and a grid size of 2.O by 2.O desrees wasdeterlnilled for this reason. The amollnt of data ibF eaCh grid ranges froIIl about 2,O x 104
to l.2× 105.
lWI radar scans betlween 17.O and‑17.0
To achieve a 200‑km s、 rath, the TR酌 正desrees frO■
■the nadir using 49 ansle biIIs. Figllre l shows a cOnceptual illustration ofis fISom
this scan,rちis the rainfatt rate(mm/h)fOrgeeachral■integer indexづ
bin.Theぢ= l toづ=拘. 五↓
l is located at near ground, and兄

"is located at the storm height)iS CalCulated
ttom the following
O.25km.ρ
い1.Distance between eatt range bin is(冴equation.
25× (ぢ‑1))=ρ(0。

where Cο υ(兄1,況ぢ)iS COVariance between兄yarORぢ )iS Vattance of兄σοり( 兄1 , 免, )yaT(兄 1)× yaケ (兄ぢ)'(3)l and兄 ぁ yar(兄 1)iS h/ariance of兄 1,andⅢ β(冴)iS Calculated at loェ gitude ttom O to 360 degrees,and at

31 If万is located in a grid,angle
latitude:と36 degrees with grid size of 2.O by 2.O degrees.
bin data including this兄l is used ttr calculating(冴ρ)in thiS grid.
航■
Rain/■0‑rain discrimination for TRMM is done for each angle bin 161.弔
disc五1五nated a■gle hns are used only for calculation of ρ(冴),Figure 2 shows global
distribution of percentag6 of rain data(P)in terms of the total amount of data for each
att gttds. MIo五ta and Higuti llsed 109/O of the conditional
grid.P is less than 109/O in II■
time to accurately express the rainfall rate distribution tt a lognormal distribution tll・
The 1/alue of 10%of the conditional time is also used to ettimate ρ(冴)町 measurementwith a rain gauge network.If the percentage of the time during whch it rains,(Pt),iS
less than 10%of the total measllrement time,then 10%of the conditional time,whidh
rぶn periOds, can be used to accurately express the rainfall rate
includes rain and no―.
dstribution tt a lognOrmal distributio■TRMM βヽ
Ve also use the value of 109/o of the conditional time toestimate(冴)町IIleasllrettents,While a rain gauge can continuously measure rain ih time at a nxed pOi
lt its measRlrement is temporally
Ⅲ
TRMM can coll愉 皿ously tteasure rain in ace.B・
宝酌
discrete at a ttxed point.VeヽsRleSS that if TR酌 E IIleasuremellts at a ttxed point had/O for each gird,.WVhen P is ktts than 10°
ld have been equal to r毛taken litSequently,P woR■

100/O of the conditional time has becn applied to estimation of(冴ρ)・F i s u r e 3 s h o w S a n e x a m p( l冴) ei n od fi c ca tt te cd u lb ay t eb dl a ρc k d o t s . T hthis example is located at 139.O degrees 10ngitude alld 35,O degrees latitude,and includes‐Tokyo,Japan. The maxinlllln range of the blac・k dots co‐espollds to the IIlean■aluc of/aluc of stor正storln height―■
十its standard deviatiOn. The IIlea■とheight and its stttndard
deviatiOn in this grid are abOut 6,O km alld l.O kEl, rttpectively. The black dOts arenttedけ EqS.(1)and(2)using leastttuares it.In this itting,α l=0。 24 and α2=0,34.
M b r i t aa n d
H i g u t i 2 =a 0s 3・s 5u m fe od r t ah ta sOtca―
atαretlhl iltie2n―
k 0 3。
l 5l l i, sα
主fairly close t0 0ur result.As shown in Fig,3,the blatt dots are itted well by Eqゃ (2),and they are■ot itted well町Eq。 (1)。MOrita and Higuti shoMed that (冴ρ)giVen byEq,(2)was appropFiate for Japan 131.Our results support those of MOrita and Hisuti'srescardh.
Figures 4 alld 5 show global distribution ofl αand α2,reSpectively. In the least―squares it calculation,the accuracy of parameters(C)iS eStimtted.恥 /hite gaps in theseigures cOrrespond to grids htting large error of estimated pttameter(larger than 1000/。
of relttive error).Relat市

e eFOr iS Calculated ttom岳× 100%・Grids hJttg large error

correspond well to thOse having small P as shO、 vll in Fig. 2. This suggests that a caII
not be correctly estiIIated from a sma■ amount of rain data.

3E)iscussiOn and cOncluding reェェェarksアFigures 6 and 7 show slobal distributiOn of relative error lofandααヽhite2,reSpectively.ヽ
gaps in these ttgures cOwespond to grids having large crrOr of estimatedl αand α2(larger
than 100%Of relative error),If ρ(ど)htt dependence on regional direrences,relative errorof α
laller than thatl is always slllaller than that ofα relative error of 2αiS alWays s■2,Orof αl at a certain region. HOwever,no clear dependence on resional difFerenccs can befound in Figs. 6 and 7.
Dependence of α on angle bin was investigOted by calculating αfor each anglebin. HOwever,no clear dependence of α on ansle bin was found. 酌Fiyagawa investigateddependence of母0■elevation an81e tl,ThiS investigation shtted that when elett

angle becomes high,a becoェ les alllost constant. The results of MIiyagawa's study supportthosc Of this study.
This kind of study shO■lld use a large amount of data collected over a 19ng term.
However,the period of the present study was only fOur llonths,It is a fairly short term
for a statistical stud} The aiII1 0f this study is to illVestigate how to estimate a using
TRMM data before attempting anttysis uSing a large amollnt Of data.

Referelhceso nr a i na t t e t t a
1 1 l
K . M o r i t aa l Sl td a tI i. SH ti ig Cu at li , s t u d i e settect on earth to sate■
比e hnks in ttlicrowave and Elillilneter wavebattds,'' Transi
IECE,vol,E61,6,pp.425‑432,1978.

121D,M.A.Jones and W.M.恥 rendland, Some statistics ofinstantaneous precipitation,''3.Chmate Appl.単正
eteOr.,vol.23,pp.1273‑1285,1984.

Prediction method for rain attemation distributio[朝K.Morita and I,Higuti,'Rぬllicro and lnittLmeter品「avesデV.Electr.COmmun.Labs.,vol.24,pp.651‑668,1976.

A proposed TrOpical Rainfall Measllring,RぃF.Adler,and G̀R.North,μl」 ・SiIIlpso■
Mission(TRMM)satellite,"Bull.Amer,Meteor.,v01.69,pp.278‑295,1988.
Spatial corttlation coe齢
151T,Manabe,H.Kobayashi,T.Ihara,and Y.Furuhama;cients of rぶIl鮎1l rate intensity inferred fronl statistics of rainfall intensity alld rainattenuation,"2ヽ NN.TelecOmmlln.,vol.41,pp.463‑469,1986.
Simulation―
based anattSiS Of dependencc
i61Y.Ohsaki,K.Nakamwa,and T.Takeda,of the mean stom height measured by a spaceborlle radar On its angle fronl thenadir,!J.Atmos.9ceaniC Technol.,vol.18,pp.1127‑1135,2001.
rainfa■on eletttion
1l Y,Mittganra, Dependence of spatial cOrrelation fimction ofrate'ReviewOf
theRadio
RescarchLabs.サangleギ
v01.34,pp.13‑22,1988.

Fig. 1. Conceptual illustration of a1ltenna scanning.

Lo9(P)

150

200
Longitude

Fig.2.Global distribution of percentage of rain data(P)in terIIIs of total amount ofdata for each grid, Color bar values indcate logaFithmS of P.

Lon9: 159 de9。

; Lct: 55 de9.

ギ
．
∞ 〇．
〇 〇．
寸 〇．
困 〇〇﹂﹂〇 〇〇ｒ 半ＯＯ Ｏ ⊆ｏ や ︒ 一ギ⊆〇一〇4Rcnge(k『 1)Fig。3. An exaIIlple of the spatial cowelation function. Black dots are intted li・ om
TRMM measurements.Red and blue curw‐ es are lines ntted by Eqs。
(1)and(2),respec̲tively.

200Longitudes倒 礎spOnd鯖F屯.生 Gh皿 愉 飾 述 o■of α
ぃ Wmc8叩
Cestttated parameter(larser than 100%of rettive crror)。

盤

補盤 背躍 紆 群ゴｒ０ ０● ０す ０︑ ０■■■円日醒■■■■■■

０200
Lon9itude

Fig. 5. Global distributiOn 9f 2・
αWhite gaps correspond ttt grids haung large error of2・α
C010r bar vallles inttcate ofestimated parameter(larger thal1 100%of relative error)。

GＮ︱■■轟附︱日圏題轡■■■

Relative error of α lｒ
Ｏｔｒ
゛

︱向︱

150200Lon9itude

Fig. 6. Global distributiOn of relative error of
α gaps correspond to grids havingl.Whtelarge errOr of estimated Parameter(larger thal1 100%of relative crror).Co10r bar values
indicate 10garithms Of relative errOF,

Relative error of α2

Lon9itudeFig, 7. Cilobal distribution of relative error
α gaps correspond to grids having
2, ofWhitelarge erroF Of eStiIIIated paralleter(larger thttn 100%of rehtive error).C010r bar values
indicate 10garithns Of relative errOr.

7